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1.
We consider the initial value problem for the Fokker–Planck–Boltzmann equation namely, viewed as the Boltzmann equation with
an additional diffusion term in velocity space to describe, for instance, the transport in thermal baths of binary elastic
collisional particles. The strong solution for initial data near an absolute Maxwellian is proved to exist globally in time
and tends asymptotically in the -norm to another time dependent self-similar Maxwellian in large time. The effect of the diffusion in phase space is investigated.
It produces a diffusion process in velocity space and results in a heating process on the macroscopic fluid-dynamic observable,
accelerating the convergence of solutions to the equilibrium of a self-similar Maxwellian at a faster time-decay rate than
the Boltzmann equation. This phenomena is also observed for homogeneous Fokker–Planck–Boltzmann equations, where the time-decay
rate in the -norm to the self-similar Maxwellian is proved to be faster than exponential. Moreover, the Fokker–Planck–Boltzmann equation
is shown to converge (under an appropriate scaling) strongly to the Boltzmann equation in the process of the zero diffusion
limit. 相似文献
2.
Arieh Pistiner 《Transport in Porous Media》2007,70(3):293-304
The saturation distribution—within an anisotropic aquifer—of a pollutant discharging from an underground source is modeled
by a two-dimensional, nonlinear diffusion–convection equation. A closed form self-similar solution is obtained for the steady
saturation distribution in the immiscible zone. The results may be used to rationalize field data collected for predicting
locations of underground leakage sources in aquifers and to understand the influence of the anisotropic permeability’s parameters
on the oil distribution in the porous medium.
An erratum to this article can be found at 相似文献
3.
Vacuum impregnation is a process method in which air and native solution are removed from the porous space of a given porous material and replaced by an external solution. Vacuum impregnation is divided into two steps: Firstly, the porous material is immersed in a liquid solution and exposed to subatmospheric pressure for a given time to ensure that air trapped in the porous materials will be removed; secondly, atmospheric pressure is re-established and the external solution penetrates the pore structure of the porous material. The objective of this study was to describe the hydrodynamic mechanisms involved in vacuum impregnation of porous materials as a function of capillary number and viscosity ratio. To achieve the objectives proposed in the present study, a transparent glass micromodel 7.7 cm × 7.4 cm was first constructed using the photolithographic technique. In addition, a stainless steel vacuum tank was built. The tank top was covered with a transparent reinforced glass plate. The whole system was connected to a vacuum pump, and a conventional video camera was adapted to record the experiments. Liquid saturation was determined through the image analysis process. Capillary number and viscosity ratio were determined for the drainage and imbibition processes. For the systems studied, we conclude that transport mechanisms ranged between stable displacement and capillary fingering during the vacuum step (drainage) while transport mechanisms ranged between continuous capillary and discontinuous capillary domains during the atmospheric step (imbibition). Earlier work indicated that our proposed process should be even more efficient for realistically large systems. 相似文献
4.
V. N. Monakhov 《Journal of Applied Mechanics and Technical Physics》1999,40(3):367-374
This work is concerned with deriving generalized self-similar solutions for a thermal model of two-phase filtration in porous
media.
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 9–17, May–June, 1999. 相似文献
5.
A. A. Papin 《Journal of Applied Mechanics and Technical Physics》2008,49(4):527-536
A model problem of the motion of water and air in thawing snow is examined using the Masket-Leverett equations of two-phase
filtration. The theorem of existence of a self-similar solution is proved.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 13–23, July–August, 2008. 相似文献
6.
Yu. D. Varlamov Yu. P. Meshcheryakov M. R. Predtechensky S. N. Ul’yankin 《Journal of Applied Mechanics and Technical Physics》2007,48(1):101-108
Microdroplet absorption by two-layer porous media is studied both theoretically and experimentally. A two-dimensional model
for liquid flow from a droplet into a porous medium is presented and veri.ed based on a simultaneous numerical solution of
the Euler equations taking into account surface tension forces and the unsteady filtration equation. The effect of the structural
parameters of the two-layer porous medium (pore size in the layers, and the thickness and porosity of the layers) on the droplet
absorption is analyzed. It is shown that the presence of the second layer can have a significant effect on the droplet absorption
rate and the liquid distribution in the medium. The pore size is found to be the main parameter that governs the effect of
the second layer.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 121–130, January–February, 2007. 相似文献
7.
A mathematical model for the discharge of a gas-saturated liquid from cylindrical channels is developed. Two limiting cases
of linear and quadratic, relations between the flow friction force and the flow velocity are considered. It is established
that the process of evacuation, from a semi-infinite channel consists of two stages. In the initial stage, the flow drag can
be ignored, and the process of discharge is described by a Riemann wave solution. For the next stage, in which inertia is
insignificant, nonlinear equations are obtained and self-similar solutions are constructed for them. The problem of flow through
a slot in a tank of finite volume is solved. It is shown that the discharge proceeds either in a gas-dynamic choking regime
or in a subsonic regime, depending on the conditions inside the tank and at the outlet. Examples of numerical calculations
are given.
Institute of Mechanics, Ufa Scientific Center, Russian Academy of Sciences, Ufa 450000 Translated from Prikladnaya Mekhanika
i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 64–73, January–February, 1999. 相似文献
8.
The present note considers two problems concerning the thermocapillary motion, due to the existence of a temperature gradient,
of a weightless liquid with a parabolic dependence of the surface tension on the temperature. These problems admit self-similar
solutions (in the generalized sense) within the framework of the Navier-Stokes equations. It is noted that the solution may
not be unique.
Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 132–137, September–October, 1988. 相似文献
9.
O. V. Voinov 《Journal of Applied Mechanics and Technical Physics》1999,40(3):412-419
The unsteady-state nonlinear problem of spreading of a drop of a viscous fluid on the horizontal surface of a solid under
the action of gravity and capillary forces is considered for small Reynolds numbers. The method of asymptotic matching is
applied to solve the axisymmetrical problem of spreading when the gravity exerts a significant effect on the dynamics of the
drop. The flow structure in the drop is determined at large times in the neighborhood of a self-similar solution. The ranges
of applicability of the quasiequilibrium model of drop spreading with a dynamic edge angle and a self-similar solution are
found. It is shown that the transition from one flow model to another occurs at very large Bond numbers.
Institute of Mechanics of Multiphase Systems, Siberian Division, Russian Academy of Sciences, Tyumen’ 625000. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 59–67, May–June, 1999. 相似文献
10.
Thomas Y. Hou Congming Li Zuoqiang Shi Shu Wang Xinwei Yu 《Archive for Rational Mechanics and Analysis》2011,199(1):117-144
We investigate the singularity formation of a nonlinear nonlocal system. This nonlocal system is a simplified one-dimensional
system of the 3D model that was recently proposed by Hou and Lei (Comm Pure Appl Math 62(4):501–564, 2009) for axisymmetric 3D incompressible Navier–Stokes equations with swirl. The main
difference between the 3D model of Hou and Lei and the reformulated 3D Navier–Stokes equations is that the convection term
is neglected in the 3D model. In the nonlocal system we consider in this paper, we replace the Riesz operator in the 3D model
by the Hilbert transform. One of the main results of this paper is that we prove rigorously the finite time singularity formation
of the nonlocal system for a large class of smooth initial data with finite energy. We also prove global regularity for a
class of smooth initial data. Numerical results will be presented to demonstrate the asymptotically self-similar blow-up of
the solution. The blowup rate of the self-similar singularity of the nonlocal system is similar to that of the 3D model. 相似文献
11.
This article describes a semi-analytical model for two-phase immiscible flow in porous media. The model incorporates the effect
of capillary pressure gradient on fluid displacement. It also includes a correction to the capillarity-free Buckley–Leverett
saturation profile for the stabilized-zone around the displacement front and the end-effects near the core outlet. The model
is valid for both drainage and imbibition oil–water displacements in porous media with different wettability conditions. A
stepwise procedure is presented to derive relative permeabilities from coreflood displacements using the proposed semi-analytical
model. The procedure can be utilized for both before and after breakthrough data and hence is capable to generate a continuous
relative permeability curve unlike other analytical/semi-analytical approaches. The model predictions are compared with numerical
simulations and laboratory experiments. The comparison shows that the model predictions for drainage process agree well with
the numerical simulations for different capillary numbers, whereas there is mismatch between the relative permeability derived
using the Johnson–Bossler–Naumann (JBN) method and the simulations. The coreflood experiments carried out on a Berea sandstone
core suggest that the proposed model works better than the JBN method for a drainage process in strongly wet rocks. Both methods
give similar results for imbibition processes. 相似文献
12.
V. P. Reutov A. B. Ezersky G. V. Rybushkina V. V. Chernov 《Journal of Applied Mechanics and Technical Physics》2007,48(4):469-478
Evolution of convective structures in a thin layer of an evaporating liquid (ethanol) located under a turbulent boundary layer
of an airflow is studied experimentally and theoretically. Evolution of the structures is examined under conditions of an
increased flow velocity. A transition is found from convective cells formed in the absence of the flow to convective rolls
elongated in the streamwise direction. The theoretical analysis is performed within a two-dimensional model of the flow in
the liquid layer. The boundary conditions on the liquid surface are obtained with the use of self-similar solutions for mean
fields in the airflow. The onset and evolution of a periodic system of rolls are simulated numerically. Theoretical conclusions
are compared with experimental data.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 3–14, July–August, 2007. 相似文献
13.
A. G. Petrova 《Journal of Applied Mechanics and Technical Physics》2007,48(5):671-679
It is proved that the problem of one-dimensional motion of an emulsion under the action of thermocapillary forces has a self-similar
solution in a semi-infinite interval. The behavior of the solution is illustrated by numerical examples for aluminum-lead
emulsions, in which the carrier phase is lead or aluminum. The solution is compared with the solution of the self-similar
problem linearized in the low impurity concentration.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 61–70, September–October, 2007. 相似文献
14.
Laboratory-scale virus transport experiments were conducted in columns packed with sand under saturated and unsaturated conditions.
The viruses employed were the male-specific RNA coliphage, MS2, and the Salmonella typhimurium phage, PRD1. The mathematical model developed by Sim and Chrysikopoulos (Water Resour Res 36:173–179, 2000) that accounts
for processes responsible for removal of viruses during vertical transport in one-dimensional, unsaturated porous media was
used to fit the data collected from the laboratory experiments. The liquid to liquid–solid and liquid to air–liquid interface
mass transfer rate coefficients were shown to increase for both bacteriophage as saturation levels were reduced. The experimental
results indicate that even for unfavorable attachment conditions within a sand column (e.g., phosphate-buffered saline solution;
pH = 7.5; ionic strength = 2 mM), saturation levels can affect virus transport through porous media. 相似文献
15.
In Part I Moyne and Murad [Transport in Porous Media 62, (2006), 333–380] a two-scale model of coupled electro-chemo-mechanical phenomena in swelling porous media was derived by
a formal asymptotic homogenization analysis. The microscopic portrait of the model consists of a two-phase system composed
of an electrolyte solution and colloidal clay particles. The movement of the liquid at the microscale is ruled by the modified
Stokes problem; the advection, diffusion and electro-migration of monovalent ions Na+ and Cl− are governed by the Nernst–Planck equations and the local electric potential distribution is dictated by the Poisson problem.
The microscopic governing equations in the fluid domain are coupled with the elasticity problem for the clay particles through
boundary conditions on the solid–fluid interface. The up-scaling procedure led to a macroscopic model based on Onsager’s reciprocity
relations coupled with a modified form of Terzaghi’s effective stress principle including an additional swelling stress component.
A notable consequence of the two-scale framework are the new closure problems derived for the macroscopic electro-chemo-mechanical
parameters. Such local representation bridge the gap between the macroscopic Thermodynamics of Irreversible Processes and
microscopic Electro-Hydrodynamics by establishing a direct correlation between the magnitude of the effective properties and
the electrical double layer potential, whose local distribution is governed by a microscale Poisson–Boltzmann equation. The
purpose of this paper is to validate computationally the two-scale model and to introduce new concepts inherent to the problem
considering a particular form of microstructure wherein the clay fabric is composed of parallel particles of face-to-face
contact. By discretizing the local Poisson–Boltzmann equation and solving numerically the closure problems, the constitutive
behavior of the diffusion coefficients of cations and anions, chemico-osmotic and electro-osmotic conductivities in Darcy’s
law, Onsager’s parameters, swelling pressure, electro-chemical compressibility, surface tension, primary/secondary electroviscous
effects and the reflection coefficient are computed for a range particle distances and sat concentrations. 相似文献
16.
Yu. N. Gordeev A. E. Sandakov Yu. L. Chizhov 《Journal of Applied Mechanics and Technical Physics》2008,49(5):776-780
A problem of piston-induced displacement of one gas by another in cracks (porous media) in an axisymmetric case with a quadratic
drag law is studied. Self-similar solutions for determining the dynamic characteristics (velocity and pressure) of the displacing
and displaced gases are constructed in quadratures. The velocity and pressure are studied as functions of a self-similar variable
for several initial conditions and parameters.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 87–92, September–October, 2008. 相似文献
17.
A model of flow through a porous medium with phase transitions which permits an efficient qualitative investigation is proposed
for two fluids with sharply different (high-contrast) mobilities. It is shown that the model problem of flow toward a unit
sink is singularly perturbed and can be solved using analytic asymptotic matching methods. The nature of the singularity is
associated with violation of the condition of the flow contrast in certain zones. The solution can be unstable depending on
the direction of interphase mass transfer and the zone in which the process takes place.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 124–135, March–April, 2000.
The work was carried out with support from the European Foundation INTAS (grant No. 94-4367) and the Russian Foundation for
Basic Research (project No. 95-01-01179a). 相似文献
18.
A. A. Shutov A. A. Zakhar'yan 《Journal of Applied Mechanics and Technical Physics》1998,39(4):489-492
The problem of the jet flow of an incompressible liquid with free boundaries in an electric field is solved in the approximation
of a laminar boundary layer. An exact solution for a round jet is found in the class of self-similar solutions. In the case
of a flat slit jet, a solution is constructed in the form of a series in powers of the coordinate transverse to the plane
of symmetry. The dependence of the radius (half-width) on the longitudinal coordinate is given.
Branch of the Karpov Physicochemistry Institute, State Science Center, Obninsk 249020. Karpov Physicochemistry Institute,
State Science Center, Moscow 115523. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 12–16,
July–August, 1998. 相似文献
19.
This paper presents a general differential mathematical model to analyze the simultaneous heat and mass transfer processes
that occur in different components of an ammonia–water absorption system: absorber, desorber, rectifier, distillation column,
condenser and evaporator. Heat and mass transfer equations are considered, taking into account the heat and mass transfer
resistances in the liquid and vapour phases. The model considers the different regions: vapour phase, liquid phase and an
external heating or cooling medium. A finite difference numerical method has been considered to solve the resulting set of
nonlinear differential equations and an iterative algorithm is proposed for its solution. A map of possible solutions of the
mass transferred composition z is presented when varying the interface temperature, which enables to establish a robust implementation
code. The analysis is focused on the processes presented in ammonia–water absorption systems. The model is applied to analyze
the ammonia purification process in an adiabatic packed rectification column and the numerical results show good agreement
with experimental data. 相似文献
20.
A numerical study is performed to analyze steady laminar forced convection in a channel in which discrete heat sources covered
with porous material are placed on the bottom wall. Hydrodynamic and heat transfer results are reported. The flow in the porous
medium is modeled using the Darcy–Brinkman–Forchheimer model. A computer program based on control volume method with appropriate
averaging for diffusion coefficient is developed to solve the coupling between solid, fluid, and porous region. The effects
of parameters such as Reynolds number, Prandtl number, inertia coefficient, and thermal conductivity ratio are considered.
The results reveal that the porous cover with high thermal conductivity enhances the heat transfer from the solid blocks significantly
and decreases the maximum temperature on the heated solid blocks. The mean Nusselt number increases with increase of Reynolds
number and Prandtl number, and decrease of inertia coefficient. The pressure drop along the channel increases rapidly with
the increase of Reynolds number. 相似文献